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Question Number 115285 by mnjuly1970 last updated on 28/Sep/20

        ...♠nice   topology ♠...  suppose  ⟨S , τ ⟩ is  Baire′s  space   and                  S = ∪_(n=1) ^∞ F_n    such  that  F_n ′s  are closed sets       prove  that::     ∃ m ; F_m ^( °)  ≠ ∅   ..m.n.july           ...♣m.n.july.1970♣...

$$\:\:\:\:\:\:\:\:...\spadesuit{nice}\:\:\:{topology}\:\spadesuit... \\ $$$${suppose}\:\:\langle{S}\:,\:\tau\:\rangle\:{is}\:\:{Baire}'{s} \\ $$$${space}\:\:\:{and}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{S}\:=\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\cup}}{F}_{{n}} \:\:\:{such} \\ $$$${that}\:\:{F}_{{n}} '{s}\:\:{are}\:{closed}\:{sets}\: \\ $$$$\:\:\:\:{prove}\:\:{that}:: \\ $$$$\:\:\:\exists\:{m}\:;\:{F}_{{m}} ^{\:°} \:\neq\:\varnothing\:\:\:..{m}.{n}.{july} \\ $$$$\:\:\:\:\:\:\:\:\:...\clubsuit{m}.{n}.{july}.\mathrm{1970}\clubsuit... \\ $$

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